Basic Electrical and Electronics Engineering (EE 103) – Chapter 3

3.1 Semiconductor and Doping

This section covers the fundamental concepts of semiconductor materials and the process of doping that makes them useful in electronic devices.

What is a Semiconductor?

Based on their ability to conduct electricity, materials can be classified into three categories:

• Conductors: Materials that allow electric current to flow easily (e.g., Copper, Silver, Aluminum). They have a very large number of free electrons.
• Insulators: Materials that resist the flow of electric current (e.g., Glass, Rubber, Wood). They have virtually no free electrons.
• Semiconductors: Materials with electrical conductivity between that of conductors and insulators (e.g., Silicon (Si), Germanium (Ge)). Their conductivity can be precisely controlled.

Energy Band Theory

In an atom, electrons occupy specific energy levels. In a solid crystal, these levels merge into bands.

• Valence Band: The outermost band of electron energies. Electrons in this band are involved in bonding the atoms together.
• Conduction Band: The band of energies where electrons are free to move and conduct electricity.
• Forbidden Band (Energy Gap, E_g): The energy gap between the valence and conduction bands. No electrons can exist in this gap. The size of this gap determines the material’s electrical properties.

In conductors, the valence and conduction bands overlap, so electrons can move freely with minimal energy.

In insulators, the energy gap is very large (> 5 eV), making it extremely difficult for a valence electron to jump to the conduction band.

In semiconductors, the energy gap is small (for Si, E_g ≈1.12 eV; for Ge, E_g ≈0.72 eV), allowing electrons to jump from the valence to the conduction band with the application of thermal or electrical energy.

Intrinsic vs. Extrinsic Semiconductors

Intrinsic Semiconductor: A semiconductor in its purest form. At room temperature, some thermal energy causes a few electrons to jump into the conduction band, leaving behind a vacancy called a hole in the valence band. Both electrons and holes contribute to conduction, but the overall conductivity is low.

Extrinsic Semiconductor: A semiconductor whose conductivity has been increased by adding a small, controlled amount of impurities. This process is called doping.

Doping

Doping involves introducing impurity atoms into the semiconductor crystal lattice to increase the number of free charge carriers (electrons or holes).

N-Type Semiconductor (Negative-type):

• Created by doping a pure semiconductor (like Silicon) with a pentavalent impurity (an element with 5 valence electrons, e.g., Phosphorus, Arsenic).
• Four of the impurity’s valence electrons form bonds with neighboring silicon atoms. The fifth electron is loosely bound and can easily move to the conduction band, becoming a free electron.
• In N-type material, electrons are the majority charge carriers, and holes are the minority carriers. The impurity atoms are called donor atoms because they donate a free electron.

P-Type Semiconductor (Positive-type):

• Created by doping with a trivalent impurity (an element with 3 valence electrons, e.g., Boron, Gallium).
• The three valence electrons form bonds, but this leaves a vacancy, or hole, in the fourth bond. This hole can accept an electron from a neighboring atom, effectively causing the hole to move.
• In P-type material, holes are the majority charge carriers, and electrons are the minority carriers. The impurity atoms are called acceptor atoms because they create a hole that can accept an electron.

3.2 Introduction to Diode

A PN junction diode is the most basic semiconductor device, formed by joining a P-type semiconductor with an N-type semiconductor.

When the P-type and N-type materials are joined, a process of diffusion occurs at the junction:

• Free electrons from the N-side diffuse across the junction to the P-side to combine with holes.
• Holes from the P-side diffuse across to the N-side to combine with electrons.

This diffusion creates a region near the junction that is depleted of free charge carriers. This area is called the depletion region or space charge region.

Within this region, the immobile donor ions on the N-side are left with a net positive charge, and the immobile acceptor ions on the P-side have a net negative charge. This separation of charge creates an electric field and a potential difference across the junction known as the barrier potential (or cut-in voltage). For silicon diodes, this is approximately 0.7V, and for germanium, it is 0.3V. This potential opposes further diffusion, and an equilibrium is reached.

3.3 Characteristics of PN Junction Diode

The behavior of a diode is described by its V-I (Voltage-Current) characteristic curve, which depends on how an external voltage is applied, a process called biasing.

1. Forward Bias

Connection: The positive terminal of a voltage source is connected to the P-type side, and the negative terminal is connected to the N-type side.

Operation: The applied voltage opposes the internal barrier potential. If the applied voltage is greater than the barrier potential (e.g., > 0.7V for Si), the depletion region narrows, and a large current of majority carriers flows across the junction. The diode acts like a closed switch.

V-I Curve: The current is negligible until the voltage reaches the knee voltage (cut-in voltage), after which it increases exponentially.

2. Reverse Bias

Connection: The negative terminal of the voltage source is connected to the P-type side, and the positive terminal is connected to the N-type side.

Operation: The applied voltage aids the internal barrier potential, widening the depletion region. This prevents the flow of majority carriers. A very small current, called the reverse saturation current (I_s), flows due to minority carriers. The diode acts like an open switch.

Breakdown: If the reverse voltage is increased to a high value (the breakdown voltage), the junction breaks down, and a large reverse current flows. This can permanently damage a standard diode.

3.4 Half-wave and Full-wave Rectifiers

Rectification is the process of converting alternating current (AC) into direct current (DC). Diodes are ideal for this because they allow current to flow in only one direction.

Half-Wave Rectifier

Circuit: It consists of a single diode in series with a load resistor.

Operation:

• During the positive half-cycle of the AC input, the diode is forward-biased and conducts, allowing current to flow through the load.
• During the negative half-cycle, the diode is reverse-biased and blocks current flow.

Result: Only the positive half-cycles of the AC input appear across the load, resulting in a pulsating DC output.

Disadvantages: Inefficient (only uses half of the AC wave) and has a high ripple factor (large AC component in the output).

Full-Wave Rectifier

This type of rectifier uses both halves of the AC input cycle to produce a more continuous DC output.

1. Center-Tapped Full-Wave Rectifier:

• Circuit: Uses a transformer with a center-tapped secondary winding and two diodes.
• Operation: Diode D1 conducts during the positive half-cycle, and diode D2 conducts during the negative half-cycle. The current through the load is always in the same direction.

2. Full-Wave Bridge Rectifier:

• Circuit: Uses four diodes arranged in a bridge configuration. It does not require a center-tapped transformer.
• Operation:
• During the positive half-cycle, diodes D1 and D2 are forward-biased and conduct.
• During the negative half-cycle, diodes D3 and D4 conduct.
• Result: The current flows through the load in the same direction during both half-cycles.

Advantages: More efficient than half-wave, lower ripple factor, and does not require a center-tapped transformer, making it the most common rectifier configuration.

3.5 Zener Effect

When a PN junction is heavily reverse-biased, a large current can flow due to two breakdown phenomena:

Zener Breakdown: This occurs in heavily doped diodes at a relatively low reverse voltage (typically < 6V). The intense electric field across the narrow depletion region is strong enough to pull electrons directly from their covalent bonds, creating a large number of free carriers.

Avalanche Breakdown: This occurs in lightly doped diodes at higher reverse voltages. The electric field accelerates the few minority carriers to very high velocities. These carriers collide with atoms in the crystal lattice, knocking out more electrons. This creates a chain reaction or “avalanche” of carriers, leading to a large reverse current.

3.6 Zener Diode and its Characteristics

A Zener diode is a special type of diode designed to operate reliably in the reverse breakdown region without being damaged.

Doping: It is heavily doped to ensure a sharp, well-defined breakdown voltage, known as the Zener voltage (V_Z).

Symbol: The symbol is similar to a standard diode, but with bent “wings” on the cathode line.

Characteristics:

• In the forward-bias direction, it behaves like a normal diode.
• In the reverse-bias direction, it allows almost no current to flow until the voltage reaches V_Z. At this point, the diode “breaks down,” and the voltage across it remains nearly constant at V_Z even as the reverse current increases significantly.

3.7 Zener Diode as a Voltage Regulator

The Zener diode’s ability to maintain a constant voltage across it while in breakdown makes it ideal for voltage regulation. A voltage regulator provides a stable DC output voltage that is independent of changes in the input voltage or the load current.

Circuit: The Zener diode is connected in reverse bias, in parallel with the load (R_L). A series resistor (R_S) is used to limit the current.

Operation:

• The input voltage (V_in) must be greater than the Zener voltage (V_Z).
• The Zener diode maintains a constant voltage V_Z across the load.
• If the input voltage increases, the extra voltage is dropped across the series resistor R_S, as more current flows through the Zener diode, while the load voltage remains fixed at V_Z.
• If the load current changes, the Zener diode adjusts the current it draws to keep the total current from the source appropriate for maintaining the voltage drop across R_S, thus keeping the output voltage stable.

3.8 Bipolar Junction Transistor (BJT)

A Bipolar Junction Transistor (BJT) is a three-terminal semiconductor device used for amplification and switching. It consists of two PN junctions formed back-to-back.

Terminals: Emitter (E), Base (B), and Collector (C).

Types:

• NPN: A thin layer of P-type material is sandwiched between two layers of N-type material.
• PNP: A thin layer of N-type material is sandwiched between two layers of P-type material.

Basic Principle: A small current flowing into the base terminal controls a much larger current flowing between the collector and emitter. The collector current (I_C) is approximately proportional to the base current (I_B): I_C = β⋅I_B, where β (beta) is the current gain.

3.9 Introduction to Digital Electronics

Digital electronics is a branch of electronics that deals with signals that have discrete values, as opposed to analog electronics, which deals with continuous signals.

Analog Signal: A continuous signal where the value can vary over a continuous range (e.g., a sound wave, temperature reading).

Digital Signal: A signal that has only two discrete levels or states. These states are represented by:

• 1 (HIGH, TRUE, ON)
• 0 (LOW, FALSE, OFF)

The use of a two-state system (binary) makes digital circuits highly reliable, immune to noise, and easy to design and store information.

3.10 Logic Gates and Boolean Algebra

Logic Gates

A logic gate is a fundamental building block of a digital circuit. It performs a logical operation on one or more binary inputs to produce a single binary output.

AND Gate: The output is HIGH (1) only if all inputs are HIGH.

Boolean Expression: Q = A⋅B

OR Gate: The output is HIGH (1) if any of the inputs are HIGH.

Boolean Expression: Q = A+B

NOT Gate (Inverter): The output is the opposite of the single input.

Boolean Expression: Q = A̅

NAND Gate (NOT-AND): The output is LOW (0) only if all inputs are HIGH. It is the inverse of an AND gate.

NOR Gate (NOT-OR): The output is LOW (0) if any of the inputs are HIGH. It is the inverse of an OR gate.

XOR Gate (Exclusive-OR): The output is HIGH (1) if the inputs are different.

XNOR Gate (Exclusive-NOR): The output is HIGH (1) if the inputs are the same.

NAND and NOR gates are known as universal gates because any other logic function can be created using only NAND gates or only NOR gates.

Boolean Algebra

Boolean algebra is the mathematical system used to analyze and simplify digital logic circuits. It uses variables that can only have two values (0 and 1) and logical operators like AND (multiplication), OR (addition), and NOT (inversion).

Basic Laws and Theorems:

• Commutative Law: A+B = B+A; A⋅B = B⋅A
• Associative Law: (A+B)+C = A+(B+C); (A⋅B)⋅C = A⋅(B⋅C)
• Distributive Law: A⋅(B+C) = (A⋅B)+(A⋅C)
• De Morgan’s Theorems: These are crucial for simplifying expressions.
• A⋅B̅ = A̅ + B̅
• A+B̅ = A̅ ⋅ B̅

By applying these rules, complex logic circuits can be simplified into circuits with fewer gates, making them cheaper, faster, and more efficient.